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Self-learning kinetic Monte Carlo (SLkMC) [1] algorithm is widely
used for the simulation of the formation of nanostructures. It is relatively
simple for implementation and has low resource cost. However, sometimes on
the energy surface there are areas with low diffusion barriers of jumps
inside of the area and high barriers to jump out. Such areas are called
energy basins. When program gets inside the energy basin it models diffusion
of the system inside of the energy basin during numerous steps. Simulated
time don't grow and the algorithm becomes very inefficient.

There are various methods for acceleration of the SLkMC [2]. They
range in accuracy, resource cost and complexity. Their common feature is that
they require knowledge of the energy basin's structure. In this work we
propose our method of finding energy basins. We suppose that it will be
useful for modeling of complicated systems with various degrees of freedom.

To test our algorithm we simulated formation of the surface alloy during
deposition of Pt atoms onto stepped Cu(111) surface. Diffusion barrier for
jump of the Cu atom near embedded to the step edge Pt atom is quite low.
Therefore, there is a need for acceleration of the algorithm. Our results are
in a good qualitative agreement with experimental work wherein such process
was investigated [3].